Books on the topic 'Maximal curves'

This article deals with curve registration, which refers to methods for aligning prominent features in a set of curves by transforming their abscissa variables. It first illustrates the concepts of amplitude and phase variation schematically and with real data before defining the time-warping functions and their functional inverse. It then describes the decomposition of total mean squared variation into separate amplitude and phase components, along with an R2 measure of the proportion of functional variation due to phase in a sample of curves. It also considers landmark registration, novel ways of defining curve features, continuous registration, and methods based on structured models for amplitude and phase variation combined with more statistically oriented fitting methods such as maximum likelihood or Bayesian estimation. The article concludes with a brief survey of software resources for registration.

This article examines the ‘dispute over tangents’ between René Descartes and Pierre de Fermat, which began in 1638, by comparing their methods of constructing tangents. Descartes’s method aims at a universality, whereas Fermat’s method aims at a generality. The article begins with a discussion of Descartes’s method of tangents, which he proposed in 1637 as a way of constructing ‘all the problems of geometry’. It then considers Fermat’s method, in which he introduces a rule for finding a maximum or minimum. It also looks at Descartes’s critiques of Fermat’s method as applied to the ellipse and the hyperbola, and how Fermat arrived at the question of the ‘specific property’ of a curve by constructing the tangents to non-geometric curves.

Prices in the Roman economy were generally set by the operation of free market forces. Occasional government interventions in the form of price ceilings occurred in times of crisis, to stabilise volatile or politically important markets, or to signal moral policies. The mechanism of price formation was generally understood, but price shocks were expected to be curbed. In a similar vein, the valuation techniques developed by the Roman jurists were based on “true” prices rather than pure market prices. Even so, party autonomy in price setting was the norm. The grain market was guided to some extent for obvious political reasons, but even here there was room for private initiative. The freedom to contract was stressed as late as Diocletian, but, not much later, rampant inflation forced him to issue his edict on maximum prices, which remains an exceptional regulation in many ways.

‘It was the time when the rush for spoils filled a corner of the forest with the yelping of hounds, the cracking of whips, the flaring of torches. The appetites let loose were satisfied at last, shamelessly, amid the sound of crumbling neighbourhoods and fortunes made in six months. The city had become an orgy of gold and women.’ The Kill (La Curée) is the second volume in Zola's great cycle of twenty novels, Les Rougon-Macquart, and the first to establish Paris – the capital of modernity - as the centre of Zola's narrative world. Conceived as a representation of the uncontrollable ‘appetites’ unleashed by the Second Empire (1852–70) and the transformation of the city by Baron Haussmann, the novel combines into a single, powerful vision the twin themes of lust for money and lust for pleasure. The all-pervading promiscuity of the new Paris is reflected in the dissolute and frenetic lives of an unscrupulous property speculator, Saccard, his neurotic wife Renée, and her dandified lover, Saccard's son Maxime.

As most cancers occur in middle-aged or older adults, only a very small proportion of the overall radiotherapy workload relates to children and young people. As there is a wide spectrum of different cancer types in this age group, not only is paediatric cancer uncommon overall but each individual type is very rare. There are many ways in which to deliver radiotherapy, including advanced photon techniques, proton beam therapy, brachytherapy, and molecular radiotherapy. For these reasons, the care of children and young people requiring radiotherapy is limited to a small number of highly specialist centres. Delivery of high-quality paediatric radiotherapy requires a multiprofessional team including radiation or clinical oncologists, therapy radiographers, physicists, dosimetrists, anaesthetists, and play specialists. This team has to interact very closely with the wider paediatric and adolescent oncology multidisciplinary team, which includes oncologists, surgeons with different anatomical expertise, radiologists, and pathologists. Children, with their developing tissues and organs, are more susceptible to long-term radiation-induced complications, including second cancers, than adults. The art of paediatric radiotherapy, therefore, is to select treatment approaches which offer the maximum chance of cure while minimizing the risk of adverse effects. Careful teamwork, peer review of radiotherapy planning, and quality assurance within a clinical trial framework offer the best chances of achieving this balance. This book covers all these aspects, highlighting the need for highly specialist teams with the extensive knowledge and the broad skillset required to offer children and young people the best possible treatments.

Bones are multifunctional passive organs of movement that supports soft tissue and directly attached muscles. They also protect internal organs and are a reserve of calcium, phosphorus and magnesium. Each bone is covered with periosteum, and the adjacent bone surfaces are covered by articular cartilage. Histologically, the bone is an organ composed of many different tissues. The main component is bone tissue (cortical and spongy) composed of a set of bone cells and intercellular substance (mineral and organic), it also contains fat, hematopoietic (bone marrow) and cartilaginous tissue. Bones are a tissue that even in adult life retains the ability to change shape and structure depending on changes in their mechanical and hormonal environment, as well as self-renewal and repair capabilities. This process is called bone turnover. The basic processes of bone turnover are: • bone modeling (incessantly changes in bone shape during individual growth) following resorption and tissue formation at various locations (e.g. bone marrow formation) to increase mass and skeletal morphology. This process occurs in the bones of growing individuals and stops after reaching puberty • bone remodeling (processes involve in maintaining bone tissue by resorbing and replacing old bone tissue with new tissue in the same place, e.g. repairing micro fractures). It is a process involving the removal and internal remodeling of existing bone and is responsible for maintaining tissue mass and architecture of mature bones. Bone turnover is regulated by two types of transformation: • osteoclastogenesis, i.e. formation of cells responsible for bone resorption • osteoblastogenesis, i.e. formation of cells responsible for bone formation (bone matrix synthesis and mineralization) Bone maturity can be defined as the completion of basic structural development and mineralization leading to maximum mass and optimal mechanical strength. The highest rate of increase in pig bone mass is observed in the first twelve weeks after birth. This period of growth is considered crucial for optimizing the growth of the skeleton of pigs, because the degree of bone mineralization in later life stages (adulthood) depends largely on the amount of bone minerals accumulated in the early stages of their growth. The development of the technique allows to determine the condition of the skeletal system (or individual bones) in living animals by methods used in human medicine, or after their slaughter. For in vivo determination of bone properties, Abstract 10 double energy X-ray absorptiometry or computed tomography scanning techniques are used. Both methods allow the quantification of mineral content and bone mineral density. The most important property from a practical point of view is the bone’s bending strength, which is directly determined by the maximum bending force. The most important factors affecting bone strength are: • age (growth period), • gender and the associated hormonal balance, • genotype and modification of genes responsible for bone growth • chemical composition of the body (protein and fat content, and the proportion between these components), • physical activity and related bone load, • nutritional factors: – protein intake influencing synthesis of organic matrix of bone, – content of minerals in the feed (CA, P, Zn, Ca/P, Mg, Mn, Na, Cl, K, Cu ratio) influencing synthesis of the inorganic matrix of bone, – mineral/protein ratio in the diet (Ca/protein, P/protein, Zn/protein) – feed energy concentration, – energy source (content of saturated fatty acids - SFA, content of polyun saturated fatty acids - PUFA, in particular ALA, EPA, DPA, DHA), – feed additives, in particular: enzymes (e.g. phytase releasing of minerals bounded in phytin complexes), probiotics and prebiotics (e.g. inulin improving the function of the digestive tract by increasing absorption of nutrients), – vitamin content that regulate metabolism and biochemical changes occurring in bone tissue (e.g. vitamin D3, B6, C and K). This study was based on the results of research experiments from available literature, and studies on growing pigs carried out at the Kielanowski Institute of Animal Physiology and Nutrition, Polish Academy of Sciences. The tests were performed in total on 300 pigs of Duroc, Pietrain, Puławska breeds, line 990 and hybrids (Great White × Duroc, Great White × Landrace), PIC pigs, slaughtered at different body weight during the growth period from 15 to 130 kg. Bones for biomechanical tests were collected after slaughter from each pig. Their length, mass and volume were determined. Based on these measurements, the specific weight (density, g/cm3) was calculated. Then each bone was cut in the middle of the shaft and the outer and inner diameters were measured both horizontally and vertically. Based on these measurements, the following indicators were calculated: • cortical thickness, • cortical surface, • cortical index. Abstract 11 Bone strength was tested by a three-point bending test. The obtained data enabled the determination of: • bending force (the magnitude of the maximum force at which disintegration and disruption of bone structure occurs), • strength (the amount of maximum force needed to break/crack of bone), • stiffness (quotient of the force acting on the bone and the amount of displacement occurring under the influence of this force). Investigation of changes in physical and biomechanical features of bones during growth was performed on pigs of the synthetic 990 line growing from 15 to 130 kg body weight. The animals were slaughtered successively at a body weight of 15, 30, 40, 50, 70, 90, 110 and 130 kg. After slaughter, the following bones were separated from the right half-carcass: humerus, 3rd and 4th metatarsal bone, femur, tibia and fibula as well as 3rd and 4th metatarsal bone. The features of bones were determined using methods described in the methodology. Describing bone growth with the Gompertz equation, it was found that the earliest slowdown of bone growth curve was observed for metacarpal and metatarsal bones. This means that these bones matured the most quickly. The established data also indicate that the rib is the slowest maturing bone. The femur, humerus, tibia and fibula were between the values of these features for the metatarsal, metacarpal and rib bones. The rate of increase in bone mass and length differed significantly between the examined bones, but in all cases it was lower (coefficient b <1) than the growth rate of the whole body of the animal. The fastest growth rate was estimated for the rib mass (coefficient b = 0.93). Among the long bones, the humerus (coefficient b = 0.81) was characterized by the fastest rate of weight gain, however femur the smallest (coefficient b = 0.71). The lowest rate of bone mass increase was observed in the foot bones, with the metacarpal bones having a slightly higher value of coefficient b than the metatarsal bones (0.67 vs 0.62). The third bone had a lower growth rate than the fourth bone, regardless of whether they were metatarsal or metacarpal. The value of the bending force increased as the animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. The rate of change in the value of this indicator increased at a similar rate as the body weight changes of the animals in the case of the fibula and the fourth metacarpal bone (b value = 0.98), and more slowly in the case of the metatarsal bone, the third metacarpal bone, and the tibia bone (values of the b ratio 0.81–0.85), and the slowest femur, humerus and rib (value of b = 0.60–0.66). Bone stiffness increased as animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. Abstract 12 The rate of change in the value of this indicator changed at a faster rate than the increase in weight of pigs in the case of metacarpal and metatarsal bones (coefficient b = 1.01–1.22), slightly slower in the case of fibula (coefficient b = 0.92), definitely slower in the case of the tibia (b = 0.73), ribs (b = 0.66), femur (b = 0.59) and humerus (b = 0.50). Bone strength increased as animals grew. Regardless of the growth point tested, bone strength was as follows femur > tibia > humerus > 4 metacarpal> 3 metacarpal> 3 metatarsal > 4 metatarsal > rib> fibula. The rate of increase in strength of all examined bones was greater than the rate of weight gain of pigs (value of the coefficient b = 2.04–3.26). As the animals grew, the bone density increased. However, the growth rate of this indicator for the majority of bones was slower than the rate of weight gain (the value of the coefficient b ranged from 0.37 – humerus to 0.84 – fibula). The exception was the rib, whose density increased at a similar pace increasing the body weight of animals (value of the coefficient b = 0.97). The study on the influence of the breed and the feeding intensity on bone characteristics (physical and biomechanical) was performed on pigs of the breeds Duroc, Pietrain, and synthetic 990 during a growth period of 15 to 70 kg body weight. Animals were fed ad libitum or dosed system. After slaughter at a body weight of 70 kg, three bones were taken from the right half-carcass: femur, three metatarsal, and three metacarpal and subjected to the determinations described in the methodology. The weight of bones of animals fed aa libitum was significantly lower than in pigs fed restrictively All bones of Duroc breed were significantly heavier and longer than Pietrain and 990 pig bones. The average values of bending force for the examined bones took the following order: III metatarsal bone (63.5 kg) <III metacarpal bone (77.9 kg) <femur (271.5 kg). The feeding system and breed of pigs had no significant effect on the value of this indicator. The average values of the bones strength took the following order: III metatarsal bone (92.6 kg) <III metacarpal (107.2 kg) <femur (353.1 kg). Feeding intensity and breed of animals had no significant effect on the value of this feature of the bones tested. The average bone density took the following order: femur (1.23 g/cm3) <III metatarsal bone (1.26 g/cm3) <III metacarpal bone (1.34 g / cm3). The density of bones of animals fed aa libitum was higher (P<0.01) than in animals fed with a dosing system. The density of examined bones within the breeds took the following order: Pietrain race> line 990> Duroc race. The differences between the “extreme” breeds were: 7.2% (III metatarsal bone), 8.3% (III metacarpal bone), 8.4% (femur). Abstract 13 The average bone stiffness took the following order: III metatarsal bone (35.1 kg/mm) <III metacarpus (41.5 kg/mm) <femur (60.5 kg/mm). This indicator did not differ between the groups of pigs fed at different intensity, except for the metacarpal bone, which was more stiffer in pigs fed aa libitum (P<0.05). The femur of animals fed ad libitum showed a tendency (P<0.09) to be more stiffer and a force of 4.5 kg required for its displacement by 1 mm. Breed differences in stiffness were found for the femur (P <0.05) and III metacarpal bone (P <0.05). For femur, the highest value of this indicator was found in Pietrain pigs (64.5 kg/mm), lower in pigs of 990 line (61.6 kg/mm) and the lowest in Duroc pigs (55.3 kg/mm). In turn, the 3rd metacarpal bone of Duroc and Pietrain pigs had similar stiffness (39.0 and 40.0 kg/mm respectively) and was smaller than that of line 990 pigs (45.4 kg/mm). The thickness of the cortical bone layer took the following order: III metatarsal bone (2.25 mm) <III metacarpal bone (2.41 mm) <femur (5.12 mm). The feeding system did not affect this indicator. Breed differences (P <0.05) for this trait were found only for the femur bone: Duroc (5.42 mm)> line 990 (5.13 mm)> Pietrain (4.81 mm). The cross sectional area of the examined bones was arranged in the following order: III metatarsal bone (84 mm2) <III metacarpal bone (90 mm2) <femur (286 mm2). The feeding system had no effect on the value of this bone trait, with the exception of the femur, which in animals fed the dosing system was 4.7% higher (P<0.05) than in pigs fed ad libitum. Breed differences (P<0.01) in the coross sectional area were found only in femur and III metatarsal bone. The value of this indicator was the highest in Duroc pigs, lower in 990 animals and the lowest in Pietrain pigs. The cortical index of individual bones was in the following order: III metatarsal bone (31.86) <III metacarpal bone (33.86) <femur (44.75). However, its value did not significantly depend on the intensity of feeding or the breed of pigs.